Conventionally, diffraction gratings are spatially periodic structures that can be separated into reflection gratings and transmission gratings.
With respect to reflection gratings, the diffracted orders of interest are on the same side of the grating as the incident and reflected objects. Moreover, since reflection gratings rely upon reflection, the thickness of the actual grating generally is not an issue.
On the other hand, with respect to a transmission grating, the diffracted orders of interest and the transmitted objects are located on one side of the grating, and the incident objects are located on the other side of the grating. Due to the transmission property of the grating, transmission gratings must be thin and/or sufficiently transparent to allow useful transmission.
Conventionally, reflection gratings used in grazing-incidence geometry are very efficient for many kinds of objects (x rays, neutrons, atoms, etc.) that are normally difficult to diffract. In such circumstances, the angle between the incident object's trajectory and the grating surface (the so-called graze angle or angle of grazing-incidence) is very small.
One disadvantage of grazing-incidence reflection gratings is the large required length of the gratings (e.g., relative to the incident beam diameter). Moreover, variations in the slope of the reflection grating surface or slight misalignments lead to proportional changes in the angles of reflection and diffraction of the quantum-mechanical objects. Furthermore, any non-flatness in the grating surface reduces the spectral resolution of the grating and the imaging resolution, if the grating is part of an imaging system. Lastly, if several reflection gratings contribute to a single image or spectrum, the resolution of the image or spectrum generated by the quantum-mechanical objects is sensitive to the mutual alignment between the gratings.
On the other hand, transmission gratings are most efficient at normal incidence, since the amount of absorbing material that the quantum-mechanical objects traverse is minimized. Transmission gratings have the advantage that the transmitted (zero-order) beam is not deflected, which is very useful for integration in imaging applications. Transmission gratings used near normal incidence are forgiving in terms of non-flatness and misalignment.
For example, if the local grating surface's normal deviates from the incident beam direction by a small angle α, the diffracted beam angles will only change on the order of α(λ/p)2, with λ being the wavelength and p being the grating period. For an x-ray transmission grating the term (λ/p)2 could be as small as 10−7 to 10−8.
One disadvantage of transmission gratings, especially at shorter wavelengths, is high absorption. Another disadvantage of transmission gratings, at shorter wavelengths, is low diffraction efficiency. Even free-standing transmission gratings, where the grating consists of an alternating array of bars and non-absorbing empty space, only achieve efficiencies around 20% in first order in the x-ray band over a limited bandwidth.
Therefore, it is desirable to provide a grating that is substantially insensitive to any non-flatness in the grating surface. Moreover, it is desirable to provide a grating that is substantially insensitive to misalignment. Furthermore, it is desirable to provide a grating that has relatively low absorption. Lastly, it is desirable to provide a grating that has high diffraction efficiency over a broad band of wavelengths.